Westerly High School. Math Department. Summer Packet

Transcription

1 Westerly High School Math Department Summer Packet for students entering their JuniorSenior Year Summer Note: Enclosed, students will find a most recent SAT Non-Calculator Practice Test via The College Board Website. As with reading, continued math practice over the summer will help keep you updated and feel more confident taking the SATs this upcoming school year. Attached to the practice test is a list of additional topics found on the SAT that will be worth reviewing and the breakdown of the Math Sections found on the SAT. The following website listed below is an excellent tutorial and a free site that you are able to utilize for any review needed. - Click on Search for Subjects, Skills, and Videos found in upper left hand corner. -Type the SubjectSkill into the Box found on the Additional Topics Covered on the SAT page at the end of this packet. - Review Videos or answer practice questions found on those topics. It is the expectation that you will have this completed by the first day of school. Good Luck! We look forward to meeting you in the fall! Happy Summer! Sincerely, WHS Math Teachers

2 Math Test No Calculator MINUTES, QUESTIONS Turn to Section of your answer sheet to answer the questions in this section. For questions -, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions -, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work.. The use of a calculator is not permitted.. All variables and expressions used represent real numbers unless otherwise indicated.. Figures provided in this test are drawn to scale unless otherwise indicated.. All figures lie in a plane unless otherwise indicated.. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f(x) is a real number. r A = pr C = pr l A = lw w h b A = bh b c a c = a + b x s s x x s Special Right Triangles l V = lwh h w r V = pr h h r V = pr The number of degrees of arc in a circle is. The number of radians of arc in a circle is p. The sum of the measures in degrees of the angles of a triangle is. h r V = pr h h w l V = lwh

3 x+ x+ x+ x = + x+ x In the equation above, what is the value of x? A) B) C) D)... Distance traveled (feet) d Time (minutes) The graph above shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctly relates d and m? A) d =m B) d = m C) d = m+ D) d = m+ m

4 The formula below is often used by project managers to compute E, the estimated time to complete a job, where O is the shortest completion time, P is the longest completion time, and M is the most likely completion time. O+ M+ P E = Which of the following correctly gives P in terms of E, O, and M? A) P =E O M B) P = E+ O+M O+ M+ E C) P = O+M E D) P = S R x V T In the figure above, RT = TU. What is the value of x? A) B) C) D) U... The width of a rectangular dance floor is w feet. The length of the floor is feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of w? A) w + B) w + C) w + D) w +w y >x x > Which of the following consists of the y-coordinates of all the points that satisfy the system of inequalities above? A) y > B) y > C) y > D) y >

5 x+ + = x+ What is the solution set of the equation above? A) { } B) {} C) {, } D) {,, } f( x) = x x gx ( ) = x x Which of the following expressions is equivalent to f( x), for x >? gx ( ) A) B) C) D) x + x + x + xx ( ) x + xx ( +) x +... ( x ) + ( y+ ) = In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates (, ).IfPQ is a diameter of the circle, what are the coordinates of point Q? A) (, ) B) (, ) C) (, ) D) (, ) A group of people went on an overnight camping trip, taking tents with them. Some of the tents held people each, and the rest held people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were -person tents? A) B) C) D)

6 O y Which of the following could be the equation of the graph above? A) y = x( x )( x+) B) y = x ( x )( x+ ) C) y = x( x+)( x ) D) y = x ( x+ )( x ) a If = b, what is the value of b a? A) B) C) D) x... Oil and gas production in a certain area dropped from million barrels in to. million barrels in. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions f best models the production, in millions of barrels, t years after the year? A) f () t = t + B) f () t = t + C) f () t = t + D) f () t = t +

7 y = x +x y x+= How many solutions are there to the system of equations above? A) There are exactly solutions. B) There are exactly solutions. C) There is exactly solution. D) There are no solutions.... gx ( ) =x hx ( ) = gx ( ) The functions g and h are defined above. What is the value of h ()? A) B) C) D)

8 Grid in result. Fraction line Write answer in boxes. For questions -, solve the problem and enter your answer in the grid, as described below, on the answer sheet.. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.. Mark no more than one circle in any column.. No question has a negative answer.. Some problems may have more than one correct answer. In such cases, grid only one answer.. Mixed numbers such as must be gridded as. or. (If is entered into the grid, it will be interpreted as, not.). Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid. Answer: Acceptable ways to grid are: Decimal point Answer:.... Answer: either position is correct NOTE: You may start your answers in any column, space permitting. Columns you don t need to use should be left blank.

9 x + x = If a is a solution of the equation above and a >, what is the value of a? The sum of x + x+ written in the form ax + bx + c and x +x can be, where a, b, and c are constants. What is the value of a+ b+ c? x + y =. x+ y =. If ( xy, ) satisfies the system of equations above, what is the value of y?... A start-up company opened with employees. The company s growth plan assumes that new employees will be hired each quarter (every months) for the first years. If an equation is written in the form y = ax+ b to represent the number of employees, y, employed by the company x quarters after the company opened, what is the value of b? B x A Note: Figure not drawn to scale. In the circle above, point A is the center and the length of arc BC is of the circumference of the circle. What is the value of x? C STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section.

10 Additional Topics Worth Reviewing for the SAT: (broken down by the areas of focus found on the SAT) Heart of Algebra: Solving Linear Equations Polynomial and Algebraic Fractions Algebraic Inequalities Factoring Quadratic Equations The Parabola and its Equations Systems of Equations Graphing Linear Systems Problem Solving and Data Analysis: Working with Percent Rate Problems Linear and Exponential Functions Understanding Graphs and Tables Proportional Relationships Passport to Advanced Math: Rational Exponents The Parabola and Their Equations Reflecting and Translating Function Graphs Nonlinear systems of equations Additional Topics in Math: Reviewing Basic Geometry Facts o Parallel Lines and Transversals, Triangle Sum Theorem Basic Trigonometry

11 Breaking Down the MATH Portion of the SAT Test Feature Redesigned SAT Math Test Time minutes Number of Sections Two; One -minute calculator section and one - minute no-calculator section Number of Questions = multiple choice+ grid-in Calculators Point penalty for wrong answer? Permitted for longer math section only No Multiple Choice Questions answer choices (A to D) Point Value Math Content Each question counts as point Greater focus on three key areas: algebra, problem solving and data analysis, and advanced math More Algebra and Trig. Topics, more multistep problems, and more problems with real world setting. Stronger connection to college-bound high school math courses What Math Content Groups are Tested? Heart of Algebra- Linear Equations and Functions Problem Solving and Data Anaylsis- ratios, proportional relationships, percentages, complex measurements, graphs, data interpretation, and statistical measures Passport to Advanced Math- analyzing and working with advanced expressions Additional Topics in Math- Essential geometric and Trigonometric relationships What types of Math Questions are asked? Multiple Choice with possible answer choices Student-Produced response questions (grid-in)

12 Breaking Down the Two Math Sections Calculator Math Section minutes M.C+ grid-ins= questions No-Calculator Math Section minutes MC + grid-ins= questions Video Link to break down Math Sections (through College Board): Calculator Policy: What is Given to Students on Cover of Both Math Sections: